On Gauged Renormalisation Group Transformations of Lattice Fermions

TL;DR

This paper introduces an exact gauged renormalisation group transformation for lattice fermions, enabling multigrid algorithms and improved chiral fermion simulations in lattice QCD.

Contribution

It develops a hierarchy of lattice fermions using Schur complements, facilitating multigrid algorithms and implementing Ginsparg-Wilson chiral fermions with dynamical gauge fields.

Findings

Constructed a hierarchy of lattice fermions via Schur complements.

Demonstrated an exact gauged renormalisation group transformation.

Enabled full multigrid algorithms for lattice quarks.

Abstract

We construct a hierarchy of lattice fermions, where the coarser lattice Dirac operator is the Schur complement of the block UL decomposition of the finer lattice operator. We show that the construction is an exact gauged renormalisation group transformation of the lattice action. In particular, using such a transformation and the QCDLAB tool, it is shown how to implement the Ginsparg-Wilson strategy for chiral fermions in the presence of a dynamical gauge field. The scheme allows, for the first time, a full multigrid algorithm for lattice quarks.